The late header was Giroud's 17th Premier League goal as a substitute for the North Londoners, equalling a single-club record set by former Manchester United forward Ole Gunnar Solskjaer.
The France striker has yet to start a league game this season and media reports before the match had suggested he could be loaned out in January to secure more playing time ahead of the 2018 FIFA World Cup in Russia.
"He is important. Why should we lose an important player? It is up to us," said Wenger.
"He will start more games. I believe as well it's always the same when you have many good players, some of them cannot play," added Wenger.
"The question you get is always 'why does the guy who is good not play?'. Because if you take him on, you have another guy who is good who will not play. It is as simple as that."
Wenger said he considered Giroud a regular member of his team and praised his attitude.
"We have to be grateful that he is part of a great team and one who can come on and make a difference with the right attitude and ability. He is a talent," he said of his compatriot.
Wenger was critical, however, of his players' slow start in recent matches and of what he saw as a creeping amount of time-wasting.
"I feel the waste of time becomes a real problem in England," he said.
"First of all I think it's in the head of the players to respect the game and to play. And secondly the authority of the referees to act early in the game because it becomes really a problem in the last two seasons."
Arsenal's previous league match was a 3-1 home defeat to Manchester United, with the Gunners conceding twice in the opening 11 minutes.
They could have been 2-0 down in the first 10 minutes at St Mary's, with Charlie Austin putting the hosts ahead in the third and missing further opportunities.
"I felt the Manchester United game played a bit of a part in the head of our defenders," Wenger told the BBC.
"They were a bit apprehensive to start well again and that's why it is sometimes not good to talk about the problem because you create a bigger one."